A rectangle is a four-sided polygon with opposite sides that are equal in length and four right angles. The formula for the perimeter and area of a rectangle can be derived from its properties.

Properties of Rectangles

Opposite sides are equal in length
Each angle is a right angle (90 degrees)
Diagonals are equal in length and bisect each other

Formulas

The perimeter (P) of a rectangle is the sum of all its sides:

P = 2 * (length + width)

The area (A) of a rectangle is given by:

A = length * width

Example Problems

1. Find the perimeter and area of a rectangle with length 5 units and width 3 units.

Perimeter (P) = 2 * (5 + 3) = 2 * 8 = 16 units

Area (A) = 5 * 3 = 15 square units

2. A rectangle has a perimeter of 24 cm and a length of 7 cm. Find its width and area.

24 = 2 * (7 + w) (Solve for w)

w = 5 cm

Area (A) = 7 * 5 = 35 square cm

Study Guide

When studying rectangles, make sure to understand the properties of rectangles, including their sides, angles, and diagonals. Practice using the formulas for finding the perimeter and area of a rectangle, and solve various example problems to reinforce your understanding. Additionally, learn to apply the concept of rectangles to real-world problems, such as calculating the area of a rectangular room or finding the perimeter of a rectangular garden.

Remember to always label the sides and angles of the rectangle correctly when solving problems, and pay attention to units when working with real-world applications.

Finally, practice drawing and visualizing rectangles to solidify your understanding of their properties and how the formulas for perimeter and area apply to different cases.

◂Math Worksheets and Study Guides Eighth Grade. Ratios, proportions and percents

Study Guide

Ratios, proportions and percents

Worksheet/Answer key

Ratios, proportions and percents

Worksheet/Answer key

Ratios, proportions and percents

Worksheet/Answer key

Ratios, proportions and percents

Worksheet/Answer key

Ratios, proportions and percents

The resources above cover the following skills:

Number and Operations (NCTM)

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Understand and use ratios and proportions to represent quantitative relationships.

Compute fluently and make reasonable estimates.

Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.

Geometry (NCTM)

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects.

Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.

Measurement (NCTM)

Apply appropriate techniques, tools, and formulas to determine measurements.

Solve problems involving scale factors, using ratio and proportion.

Solve simple problems involving rates and derived measurements for such attributes as velocity and density.

Grade 8 Curriculum Focal Points (NCTM)

Geometry and Measurement: Analyzing two- and three-dimensional space and figures by using distance and angle

Students use fundamental facts about distance and angles to describe and analyze figures and situations in two- and three-dimensional space and to solve problems, including those with multiple steps. They prove that particular configurations of lines give rise to similar triangles because of the congruent angles created when a transversal cuts parallel lines. Students apply this reasoning about similar triangles to solve a variety of problems, including those that ask them to find heights and distances. They use facts about the angles that are created when a transversal cuts parallel lines to explain why the sum of the measures of the angles in a triangle is 180 degrees, and they apply this fact about triangles to find unknown measures of angles. Students explain why the Pythagorean Theorem is valid by using a variety of methods - for example, by decomposing a square in two different ways. They apply the Pythagorean Theorem to find distances between points in the Cartesian coordinate plane to measure lengths and analyze polygons and polyhedra.